Robustness and efficiency of Rosenbaum's rank-based estimator in randomized trials: a design-based perspective

• 成果类型: Article
• 署名作者: Ghosh, Aditya; Deb, Nabarun; Karmakar, Bikram; Sen, Bodhisattva
• 署名单位: Stanford University; University of Wisconsin System; University of Wisconsin Madison; Columbia University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444; 1464-3510
• DOI: 10.1093/biomet/asag028
• 发表日期: 2026
• 页码: asag028
• 关键词: breakdown point; Causal Inference; covariate adjustment; Hodges-Lehmann 0.864 lower bound; Local asymptotic normality; randomization inference; Wilcoxon rank-sum test; regression adjustments; sensitivity; inference

摘要

Mean-based estimators of causal effects in randomized experiments may behave poorly if the potential outcomes have a heavy tail or contain outliers. An alternative estimator proposed by estimates a constant additive treatment effect by inverting a randomization test using ranks. We develop a design-based asymptotic theory for this rank-based estimator and study its robustness and efficiency properties. We show that Rosenbaum's estimator is robust against outliers with a breakdown point that uniformly dominates that of any weighted quantile estimator. When pretreatment covariates are available, a regression-adjusted version of Rosenbaum's estimator uses an agnostic linear regression on the covariates and bases inference on the ranks of residuals. Under mild integrability conditions, we show that this estimator is at most 13.6% less efficient, in the worst case, than the commonly used mean-based regression adjustment method proposed by , and often outperforms it when the residuals have heavy tails. Moreover, under suitable assumptions, Rosenbaum's regression-adjusted estimator is at least as efficient as the unadjusted one. Finally, we initiate the study of Rosenbaum's estimator when the constant treatment effect assumption may be violated. To analyse the regression-adjusted estimator, we develop local asymptotics of rank statistics under the design-based framework, which may be of independent interest.